RevisionDojo

SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR - IB Questionbank | RevisionDojo

Practice SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

The heights (in cm) of 50 plants are recorded in the following frequency table:

Height $(\mathrm{cm})$	Frequency
$20 \leq h<30$	10
$30 \leq h<40$	15
$40 \leq h<50$	12
$50 \leq h<60$	8
$60 \leq h<70$	5

Estimate the mean height of the plants.

[3]

Determine the modal class.

[1]

Estimate the probability that a randomly selected plant has a height of at least 50 cm.

[2]

Question 2

SL & HLPaper 1

The scores, $x$ , obtained by $15$ students in a Mathematics quiz are shown below. $32, 45, 28, 39, 41, 35, 25, 48, 30, 42, 38, 36, 40, 33, 44$

Find the median score.

[2]

Find the lower quartile and the upper quartile of the scores.

[4]

Calculate the interquartile range of the scores.

[1]

Question 3

SL & HLPaper 1

A dataset consists of the numbers $x_{1}, x_{2}, \ldots, x_{n}$ , with mean $\bar{x}$ and standard deviation $s$ .

If each number is increased by a constant $c$ , show that the new mean is $\bar{x}+c$ .

[2]

If each number is increased by $c$ , show that the new standard deviation is $s$ .

[2]

If each number is multiplied by a constant $k$ (where $k>0$ ), show that the new variance is $k^{2} s^{2}$ .

[3]

Question 4

SL & HLPaper 1

A dataset consists of $n$ values $x_{1}, x_{2}, \ldots, x_{n}$ , with mean $\bar{x}$ and variance $s^{2}$ . A new dataset is created by applying the transformation $y_{i}=a x_{i}+b$ , where $a>0$ and $b$ are constants.

Show that the mean of the new dataset is $a \bar{x}+b$ .

[2]

Show that the variance of the new dataset is $a^{2} s^{2}$ .

[3]

If $a=2, b=5$ , and the original dataset has $\bar{x}=10$ and $s=4$ , calculate the mean and standard deviation of the new dataset.

[2]

Prove that the interquartile range (IQR) of the new dataset is $a$ times the IQR of the original dataset.

[3]

Question 5

SL & HLPaper 1

Consider four integers $a$ , $b$ , $c$ , and $d$ such that $a<b<c<d$ .

Let $a<b<c<d$ where the maximum is twice the range, and the median is 10. Find the value of $a$ for which the mean is 11.

[4]

Let $a$ and $d$ be the same as your answers to part (a), but $b$ and $c$ have been altered. If $a,b,c,d$ create a geometric sequence, find the median.

[4]

Question 6

SLPaper 1

Consider three integers $a$ , $b$ , $c$ which follow an arithmetic sequence respectively.

Show that $b$ is the mean of $a$ and $c$

[2]

if $2b$ is the range, find $a$

[2]

A student said that this forms a geometric sequence of common ratio 2, is that correct? Explain why or why not.

[2]

Question 7

SL & HLPaper 2

The scores of $10$ students on a short mathematics test are recorded below.

$65, 72, 80, 68, 75, 82, 70, 78, 60, 70$ .

Find the mean and standard deviation of these scores.

[4]

Question 8

SL & HLPaper 2

The times in minutes for seven students to complete a logic puzzle were measured. The results are shown below.

$25, 30, 28, 120, 22, 35, 20$

Find the mean and standard deviation of these times.

[4]

State which of the mean, median or mode you consider would be most appropriate to use as a measure of central tendency to represent the data in this case.

[1]

For each of the two measures of average you did not choose in part (ii), give a reason why you consider it inappropriate.

[2]

Question 9

SL & HLPaper 2

A set of $N$ observations, $x$ , is coded using $y = x - 45$ . It is found that $\sum y = 100$ and $\sum y^2 = 1000$ . Given that the standard deviation of $x$ is $5$ .

Find the number of observations, $N$ .

[3]

An additional observation, $x_{N+1}$ , is added to the set. The new mean of the $N+1$ observations is $50.5$ .

Find the value of $x_{N+1}$ .

[3]

Calculate the standard deviation of all $N+1$ observations.

[4]

Question 10

SL & HLPaper 2

The daily number of visitors to a small art gallery, chosen at random during a certain month, were found to be:

$120, 150, 130, 140, 160, 125, 135, 145, 1000, 120, 140$ .

Choose and Calculate an appropriate measure of central tendency (mean, mode or median) to summarise these visitor numbers. Explain briefly why the other measures are not suitable.

[5]

SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR Questionbank